Verify that the following function is a probability mass function, and determine the requested probabilities. 4x+2 50' Is the function a probability mass function? Give exact answers in form of fraction (a) P(X 4) (b) P(X s 1)- (c) P(2 s X <4) (d) P(X> -10) Statistical Tables an
Question 1. A Discrete Distribution - PME Verify that p(x) is a probability mass function (pmf) and calculate the following for a random variable X with this pmf 1.25 1.5 | 1.7522.45 p(x) 0.25 0.35 0.1 0.150.15 (a) P(X S 2) (b) P(X 1.65) (c) P(X = 1.5) (d) P(X<1.3 or X 221) e) The mean (f) The variance. (g) Sketch the cumulative distribution function (edf). Note that it exhibits jumps and is a right continuous function.
12 Verify that the following function is a probability mass function, and determine the requested probabilities. [Give exact answers in form of fraction.] f(x)-(5/6)(1/6)" x=0,1,2, , (a) P(X= 2) (b) P(X s 2)-.uI = i (c) P(X > 2)= (d) P(X21) = T Your answer is partially correct. Try again. Verify that the following function is a probability mass function, and determine the requested probabilities f (x)3x+3 45x 0, 1, 2,3,4 Is the function a probability mass function? Give exact...
function Ckek osrs4 be a density 4. Let f(x)=3 otherwise Find: i) k = 24] P(-2<x<2)
1. Verify that fxr (x,y) -2e-x-y 0 < x < 00, x < y < is joint probability density function 2. Compute the probability that X < 1.and Y < 2.
Consider the following PMF for a continus random variable f(x) = 0,25-Kx®2 Calculate K Calculate P(3<x<5) Calculate P(X <= 4) Calculate E(X) Calculate Var(X)
Determine the value of such that the function f (x, y) = cxy for 0<x<3 and 0 <y<3 satisfies the properties of a joint probability density function. Determine the following. Round your answers to four decimal places (e.g. 98.7654). 1.0994 P&<2,Y<3) 7.4444 P(X<2.0) 21:1878 Pu<Y<1,7) 12489 P(X>1.8,1 <Y<2.5) 7:3733 EX) P(X < 0,8< 4)
4-1. Suppose that f(x)-e-x for 0 < x. Determine the fol- lowing probabilities: (c) P(X= 3) (e) P(3 s x) (d) P(X<4)
(1) Suppose that X is a continuous random variable with probability density function 0<x< 1 f() = (3-X)/4 i<< <3 10 otherwise (a) Compute the mean and variance of X. (b) Compute P(X <3/2). (c) Find the first quartile (25th percentile) for the distribution.
5. Let X be a discrete random variable. The following table shows its possible values associated probabilities P(X)( and the f(x) 2/8 3/8 2/8 1/8 (a) Verify that f(x) is a probability mass function. (b) Calculate P(X < 1), P(X 1), and P(X < 0.5 or X >2) (c) Find the cumulative distribution function of X. (d) Compute the mean and the variance of X.